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It is transversal in the sense that it is performed by broadcasting the physical operation over the physical qubits of the logical qubit. And often this is fault tolerant. ...but yes I agree and the blog post makes this exact point. It is conditionally transversal, not truly transversal.

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The Z stabilizers are needed to check for physical X errors. Immediately after a measurement that's fine because X errors do nothing to X eigenstates. But once you do the transversal T the X errors start to matter so you need to be able to check for them. So you need the Z stabilizers back before T.

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A Z basis stabilizer that touches qubit q does not commute with an X basis measurement of q. If you measure the stabilizer before the measurement and after the measurement, you don't get the same result. In a transversal X measurement this happens to all Z stabilizers.

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Craig Gidney @craiggidney.bsky.social · 31/03/2026

My dream paper is a zero-knowledge proof that I know the answer to the Collatz conjecture.

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This is from a paper that should have appeared on arXiv today but due to technical issues will only be there tomorrow; for the moment it's at quantumai.google/static/site-... See also this blog post on the idea: research.google/blog/safegua...

quantumai.google

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Craig Gidney @craiggidney.bsky.social · 31/03/2026

As timelines tighten, details might benefit attackers more than defenders. So we're trying something weird: proving a circuit exists without revealing it. For example, here's a zero-knowledge proof that we found 10x smaller quantum circuits for ECDLP: github.com/tanujkhattar...

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Craig Gidney @craiggidney.bsky.social · 28/03/2026

There's support for making SVG diagrams of circuits, and there are existing tools to convert SVGs into TikZ.

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Craig Gidney @craiggidney.bsky.social · 28/03/2026

While I was attending APS March Meeting, I appeared in the 632nm podcast. The recording is available on youtube: www.youtube.com/watch?v=lnHg... Never been on a podcast before, and no doubt that shows, but it was fun.

youtube.com

How To Make Quantum Algorithms Cheaper | Craig Gidney on Magic-State Factories, Resource Estimates

YouTube video by 632nm

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Craig Gidney @craiggidney.bsky.social · 25/03/2026

I would bet against Q day by 2030, but I wouldn't bet against it at 10:1 odds. ~10% risk is unacceptably high here, so I'm very in favor of transitioning to quantum-safe cryptography by 2029: blog.google/innovation-a... Yes this means I 90% expect to be made fun of in 2030. Oh well.

blog.google

Quantum frontiers may be closer than they appear

An overview of how Google is accelerating its timeline for post-quantum cryptography migration.

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Craig Gidney @craiggidney.bsky.social · 23/03/2026

I have to admit, reading the abstract, I don't understand how this differs from what McKague+ showed in 2008 (or equivalently what I described in my blog post). Eve can pass any test for complex gates using only real gates if she has pre-distributed some constant-sized entangled catalysts.

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Craig Gidney @craiggidney.bsky.social · 17/03/2026

The slides from my talk "how to eat magic states" at APS 2026: docs.google.com/presentation... ...The content of the talk definitely drifted from when I picked the title. Mostly I talked about realizing I didn't understand reaction depth a few months ago.

docs.google.com

[APS2026] How to eat magic states

How to eat magic states APS March Meeting 2026 Craig Gidney Google Quantum AI Hello everyone, My name is Craig and my talk is called "how to eat magic states". Now... I have a bit of a confession. The...

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Craig Gidney @craiggidney.bsky.social · 19/02/2026

Whoops, I missed that they have multiple shots. The gate overhead is ~5600x not 256x.

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Craig Gidney @craiggidney.bsky.social · 19/02/2026

Chevignard et al show residues also reduce the qubit cost of quantum attacks on elliptic curves: eprint.iacr.org/2026/280 The space savings is less dramatic than for factoring (1.6x instead of 6x), and they again pay a big gate count penalty (256x), but very interesting.

eprint.iacr.org

Reducing the Number of Qubits in Quantum Discrete Logarithms on Elliptic Curves

Solving the Discrete Logarithm problem on the group of points of an elliptic curve is one of the major cryptographic applications of Shor's algorithm. However, current estimates for the number of qubi...

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Craig Gidney @craiggidney.bsky.social · 16/02/2026

Made a video tutorial of using crumble to create a quantum error correction circuit: youtu.be/SnpLSvyyEx8

youtu.be

How to make Quantum Error Correction circuits with Crumble

YouTube video by Craig Gidney

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And, of course, if you're in charge of some security thing that's vulnerable to quantum attacks, you should be *assuming progress*. The strategy "we'll start our 3 year plan when it looks 4 years away" is just guaranteeing an "oh shit" moment when progress subtracts 2 years.

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The cost of holding assumptions constant is they go stale. In 2012, demanding 1e-3 noise was audacious. Now it's conservative. Locality? The mechanisms for long-range connections are multiplying and improving. Frankly, if you assume *progress*, 100k qubits starts looking high.

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Factoring 2048-bit RSA Integers in 177 Days with 13436 Qubits and a Multimode Memory

This might be unappreciated outside the field, but it's easy to juice numbers by demanding more from hardware. It's a common type of paper (e.g. arxiv.org/abs/2103.06159 and arxiv.org/abs/2302.06639). To avoid this confounder. I've tried to hold my assumptions constant over time.

arxiv.org

We analyze the performance of a quantum computer architecture combining a small processor and a storage unit. By focusing on integer factorization, we show a reduction by several orders of magnitude o...

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The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes

I've been asked several times to comment on arxiv.org/abs/2602.11457, which claims to reduce the qubit cost of factoring by 10x. My take is that they demand a *lot* more qubit connectivity for that number. Your mileage depends entirely on how plausible you find those demands.

arxiv.org

The realisation of utility-scale quantum computing inextricably depends on the design of practical, low-overhead fault-tolerant architectures. We introduce the \textit{Pinnacle Architecture}, which us...

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Craig Gidney @craiggidney.bsky.social · 04/02/2026

From having seen Austin explain the surface code many times: this makes sense to me as the progression he'd chose. He's known surface codes so long that the complications become hard to perceive. And with prerecorded lectures the students can't stop the runaway train with "wait what?" questions.

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Craig Gidney @craiggidney.bsky.social · 04/02/2026

Yup, it's a bit like zooming way in on the boundary of a hyperbolic code. Except I think those don't have a boundary at the edge, but instead have non-local links to other sections of the edge. Otherwise you can't get the constant coding rates they advertise.

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Craig Gidney @craiggidney.bsky.social · 04/02/2026

I use *programming* to generate images. I like SVG as a target format because it's so easy to generate programmatically from any language. In this case I was calling stuff I'd previously written to draw the stabilizers of a code. So I just picked qubit locations and stabilizer bases.

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Craig Gidney @craiggidney.bsky.social · 03/02/2026

A surface code that goes from a normal tiling to one where each row keeps using half as many qubits as the last. I can't think of a reason to do this, but it's visually interesting.

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Craig Gidney @craiggidney.bsky.social · 21/01/2026

Or someone has to endorse you. TBH I thought this was already how it worked. For my first submission nine years ago I had to get an endorsement. I got it from Dave Bacon. It looks like the main change is that previously endorsement was skipped if your email address was associated with a university.

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Craig Gidney @craiggidney.bsky.social · 19/01/2026

In other words: Early Fault Tolerance starts when quality transitions from an impassable barrier to a mere tradeoff. Concretely… I arbitrarily declare EFT begins once it's demonstrably possible to do T gates with an infidelity of 10^-10. You mostly won't do T gates that way... but you *could*.

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Craig Gidney @craiggidney.bsky.social · 19/01/2026

To me it refers to the quality problem being solved while the quantity problem remains. So you *could* perform universal logical gates far better than you could ever need... but you can't hold a lot of qubits at once. Sacrificing quality to gain a bit of quantity is then a natural tradeoff.

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Craig Gidney @craiggidney.bsky.social · 02/01/2026

Stim pushed the field forward... but I worry it may also hold it back. For example, Stim doesn't understand adaptive strategies like "measure again if you see a suspicious thing". If too many researchers rely on stim, adaptivity will be under-explored!

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Craig Gidney @craiggidney.bsky.social · 02/01/2026

Papers citing stim doubled again in 2025. Stim is a python package for analyzing/simulating quantum error correction circuits. It was thousands of times faster than prior tools and popularized modelling fault tolerance in terms of "detectors" (see quantum-journal.org/papers/q-202...).

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Craig Gidney @craiggidney.bsky.social · 30/12/2025

Better simulations of magic state cultivation: scirate.com/arxiv/2512.2... . In my initial paper, I approximated T with S by using a 2x safety factor measured at d=3. IMO this paper suggests another 2x at d=5. They *claim* another 7.65x; an attempts-vs-error curve would help tell.

scirate.com

SOFT: a high-performance simulator for universal fault-tolerant quantum circuits

Circuit simulation tools are critical for developing and assessing quantum-error-correcting and fault-tolerant strategies. In this work, we present SOFT, a high-performance SimulatOr for universal Fau...

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Craig Gidney @craiggidney.bsky.social · 29/12/2025

I always pictured it as more of a bullet-holes-filling-in type of thing, because the stabilizers are being constantly recreated.

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Craig Gidney @craiggidney.bsky.social · 26/12/2025

It's a good example of the type of growth to expect, qualitatively speaking. If the same thing does play out for full quantum codes over the next few years, then the better story would be that. But that hasn't happened yet.

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Craig Gidney @craiggidney.bsky.social · 25/12/2025

An upbeat blog post for Christmas: Quantum Error Correction goes FOOM algassert.com/post/2503

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Gah, it should be 1% not 0.1% in 2014.

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This pattern is why I expect logical qubits (in full quantum codes not just rep codes) to go from barely better than the raw physical qubits to ridiculously amazing within years, despite it taking decades to get to the current level.

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The error rate doesn't change smoothly; it's driven by crossing barriers. Are you below threshold? Are you removing leakage? Are you mitigating cosmic rays? Even ignoring barriers, qubits growing exponentially vs time would imply super-exponential growth in suppression (i.e. "foom").

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